Even as members of his own party weigh whether Congress has the authority to push back on his trade actions, President Donald Trump on Tuesday slapped new tariffs on solar panels and washing machines.

“It will provide a strong incentive for LG and Samsung to follow through on their recent promises to build major manufacturing plants for washing machines right here in the United States,” Trump said during an Oval Office signing event, adding the actions “uphold a principle of fair trade and demonstrate to the world that the United States will not be taken advantage of anymore.” That echoes a major theme of his 2016 campaign and the first year of his presidency.

But Republican Sen. Ben Sasse of Nebraska issued a statement on Tuesday warning the president against the new tariffs, and other GOP senators openly mused about seeking ways to insert themselves into a testy trade debate.

“Here’s something Republicans used to understand: Tariffs are taxes on families,” he said. “Moms and dads shopping on a budget for a new washing machine will pay for this — not big companies.”

Senate Republicans also discussed Trump’s trade stances at length during Tuesday’s weekly GOP policy lunch. Among the biggest issues raised were the possible withdrawal from the North American Free Trade Agreement and the solar panel and washing machine tariffs.

NAFTA, the action on tariffs and other announcements have “members of the United States Senate looking for ways to make sure their voices are heard on the topic of trade,” Republican Sen. Jerry Moran of Kansas said.

Senate Republican Conference Chairman John Thune of South Dakota said Tuesday that he and colleagues are “trying to push as much as we can the idea that withdrawing from NAFTA would be really bad for the economy.”

Thune, who is also chairman of the Commerce Committee and a member of the Finance Committee, which oversees trade deals, added, “I don’t know if we’ve got any member in the entire Republican conference in the Senate who doesn’t believe that withdrawing from NAFTA is a bad idea.”

One Republican senator, speaking on background to discuss private conversations, said Finance Chairman Orrin G. Hatch of Utah is exploring ways the chamber might be able to block Trump from withdrawing from NAFTA.

A spokeswoman for the panel said Hatch “continues to believe we must modernize the trilateral trade pact and that terminating or weakening NAFTA would be detrimental to the U.S. and Utah’s economy.”

There is a belief, another GOP senator said, that because NAFTA is a treaty, the chamber might be able to weigh in should Trump withdraw. Any action would likely have to occur after the administration makes a final decision, which is expected sometime in the coming months.

“It’s never been done, but I think a number of us who are concerned about the administration’s direction on trade are going to speak out loudly,” Sen. Lamar Alexander of Tennessee said.

“There is some argument both ways,” said Iowa Sen. Charles E. Grassley, who said he has pending questions before the Finance panel on the chamber’s authority in the space.

Discussions are ongoing among Senate Finance Committee staff on what actions could be taken. In the meantime, Republicans are expected to become more vocal in their frustrations over some of the administration’s decisions.

Some Republicans characterized the discussions as ways the chamber can be an active partner in the decisions.

“We’re not exploring ways to be divisive; we’re exploring ways that we can work with Trump,” Idaho Sen. Jim Risch said.

Not all Republicans are critical of Trump’s trade moves. Ohio Sen. Rob Portman joined his Buckeye State Democratic colleague, Sherrod Brown, in applauding the president for his action on home appliances.

“I am pleased that the President and the U.S. Trade Representative have taken decisive action to level the playing field and protect American jobs,” Portman, a former trade representative himself, said in a joint statement with Brown.

Brown added, “These tariffs will help level the playing field, and show anyone who tries to cheat our trade laws that they won’t get away with it. I applaud the Administration for this strong relief, and will continue to work to strengthen our trade laws so this cheating can’t happen in the first place.”

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In the meantime, the president said he has recently talked to 10 executives whose corporations soon will make major investments in the United States. (He did not name them.) And he predicted “there won’t be a trade war” because of his approach to global trade.

He slammed NAFTA and called a U.S.-South Korea trade pact a “disaster for this country.” He said “we’ll be doing other trade deals, as well,” but senior White House officials say none are planned to be started or ripped open this year.

Trump’s actions Tuesday fit under his “America First” governing philosophy and come one day before he leaves for the World Economic Forum Annual Meeting in Davos, Switzerland.

Ellyn Ferguson contributed to this report. Get breaking news alerts and more from Roll Call on your iPhone or your Android.